Studying the similarities and differences in genomic interactions between species provides fertile grounds for determining the evolutionary dynamics underpinning genome function and speciation. Here, we describe the principles of 3D genome folding in vertebrates and show how lineage-specific patterns of genome reshuffling can result in different chromatin configurations. We (1) identified different patterns of chromosome folding in across vertebrate species (centromere clustering versus chromosomal territories); (2) reconstructed ancestral marsupial and afrotherian genomes analyzing whole-genome sequences of species representative of the major therian phylogroups; (3) detected lineage-specific chromosome rearrangements; and (4) identified the dynamics of the structural properties of genome reshuffling through therian evolution. We present evidence of chromatin configurational changes that result from ancestral inversions and fusions/fissions. We catalog the close interplay between chromatin higher-order organization and therian genome evolution and introduce an interpretative hypothesis that explains how chromatin folding influences evolutionary patterns of genome reshuffling.